The PA linearization problem arises in equipment of communication systems where a PA of a transmitter operates in the saturation region providing high efficiency, but suffering from the non-linear distortions.
The problem of PA linearization is often solved by applying predistortion to the PA input signal such that the output signal of the cascade of predistorter and PA is distortionless or almost distortionless. As the predistortion is generally carried out in the digital domain, e.g., based on using digital signal processing principles, the technology is called digital predistortion and the predistortion device is called a Digital Predistorter (DPD). A DPD produces a non-linear transfer function, which is inverse to that of the PA. This action linearizes the Amplitude-to-Amplitude Modulation (AM-AM) and Amplitude-to-Phase Modulation (AM-PM) functions of the DPD and PA in cascade. A DPD is a sort of a non-linear adaptive filter, whose weights are calculated, using adaptive signal processing algorithms. Presently there are two main kinds of DPDs: DPDs with indirect learning (e.g., element 400, see FIG. 4) and DPDs with direct learning (e.g., element 500, see FIG. 5).
In FIGS. 4 and 5, x(k) 402 and 502 is the digital transmitted signal, (e.g., the output signal of a digital modem). Even the non-linear PA output signal exists in continuous time t as y(t); for simplification of notation, a discrete-time presentation is used for both continuous-time and discrete-time (e.g., time-sampled by Analog-to-Digital Converter, ADC) signals as y(k) 406 and 512, where k=0, 1, 2 . . . is the signal sample number, see FIGS. 4 and 5. The same discrete-time form is also used for other continuous signals, as described in the document. The discrete-time representation of continuous signals is useful for simplification of notation and for computer simulations of a DPD. In this case, the discrete time samples are defined as t(k)=kTS=k/FS, where FS is the sampling frequency and TS is the sampling frequency period.
In FIG. 4, scaled by the gain of the PA G0 411, the signal x′(k)=G0−1y(k) 410 comes to an input of Predistorter 401. The Predistorter 401 is a non-linear filter, whose weights are calculated on-line by means of the Adaptive Algorithm 403. The architecture of the non-linear filter depends on the PA non-linearity approximation by means of polynomials, splines, etc. Any of the non-linearity approximations can be used in the DPDs described hereinafter.
An Adaptive Algorithm 403 during its operation minimizes the Mean Square Error (MSE) cost function, based on the errors α(k) between the Predistorter Copy 407 (that is the same non-linear filter as the Predistorter 401) and the Predistorter output signals y′(k) 404 and y(k) 408.
The indirect learning DPD 400, see FIG. 4, has a few disadvantages. The output signal y(k) 406 of the PA 405 may be noisy. Because the noisy signal x′(k)=G0−1y(k) 410 is used for the calculating of adaptive filter (Predistorter) weights, the weights are biased, that leads to the DPD performance degradation. The non-linear filters (e.g., the Predistorter Copy 407 and Non-Linear PA 405) are un-permutated in cascade do not guarantee the same performance (e.g., MSE etc.) as that of the Non-Linear PA and Predistorter in cascade.
These disadvantages are absent in the direct learning DPD 500, see FIG. 5, because of the following reasons: there is no measurement noise in the input signal x(k) 502, which is used for the calculation of the adaptive filter (Predistorter 501) weights. So, there the weights do not need to be biased. The minimized MSE cost function is based on the estimation of errors α(k) 510 between the scaled PA output signal y(k)=G0−1 y″(k) 512 and the delayed by D samples x(k) signal, e.g., d(k)=x(k−D) 508, where D is the system delay, caused the Predistorter 501, Non-Linear PA 505 and some implementation issues. In this case, the error α(k) 510 is a parameter, which directly characterizes the DPD performance, e.g., MSE of the signal at the Non-Linear PA output 506.
A simplified system view of FIG. 5 is shown in FIG. 6. Here, the Predistorter 601 output signal y′(k) 604 is delivered to the input of the PA 605 of a transmitter by means of the Digital-to-Analog Converter (DAC) 607 and frequency Up-Converter 609. The feed-back signal y(k) 612 is delivered for base-band calculations by means of the frequency Down-Converter 613 and ADC 611. Thus, the above mentioned implementation issues, which produce system delay D value, depend on the delays of DAC 607, ADC 611, Up- and Down-Converters 609, 613, at least.
The details of the direct learning DPD 700 are shown in FIG. 7. A main signal path of the direct learning DPD 700 includes the DPD 701 and the non-linear PA device (in general case with memory) 717. The non-linear PA device 717 includes a linear filter 703, the non-linear PA 705 and a fourth delay element (Delay 4) 709. A second signal path of the direct learning DPD 700 includes a third delay element (Delay 3) 707. A third signal path of the direct learning DPD 700 includes a first delay element (Delay 1) 711. The input signal 702 having passed the main path of the direct learning DPD 700, e.g., the signal y(k), is subtracted by a subtraction unit 715 from the delayed input signal 702 having passed the second path to provide an error signal 712. An adaptive algorithm 713 adjusts the weights of the DPD 701 based on the input signal 702 having passed the third signal path, e.g., the delayed input signal 714 and the error signal 712.
There are two main problems as indicated below, which restrict the efficiency of the DPD 700, see FIG. 7, called hereinafter Traditional DPD.
First problem: The step-size μmax in the gradient search based Adaptive Algorithms, used in the direct learning Traditional DPD 700, has to have a smaller value, see equation (3) below, compared with the case, when both, the Adaptive Filter 701 and the Adaptive Algorithm 713 would use the same input signal x(k) 702, see equation (5) below. A smaller value of the step-size increases the duration of the transient response of the gradient search based Adaptive Algorithms, because the response is increased, if the step-size is decreased.
Second problem: The direct learning Traditional DPD 700, see FIG. 7, cannot use the Recursive Least Squares (RLS) Adaptive Algorithms which are more efficient ones compared with the gradient search based Adaptive Algorithms, because the RLS algorithms become instable in this architecture, as the algorithms do not have a parameter (like a step-size) for the stability control.
As the performance of a DPD depends on its architecture and used algorithms, there is a desire to solve the above-defined two problems and hence to improve the efficiency of DPD.
In order to describe the invention in detail, the following terms, abbreviations and notations will be used:                DPD: Digital Predistorter        PA: Power Amplifier        AM-AM: Amplitude-to-Amplitude Modulation        AM-PM: Amplitude-to-Phase Modulation        ANC: Active Noise Control        LMS: Least Mean Square (Algorithm)        RLS: Recursive Least Squares (Algorithm)        NLMS: Normalized LMS (Algorithm)        AP: Affine Projection        FAP: Fast AP        VSS: variable Step-Size        MSE: Mean Square Error        PSD: Power Spectral Density        